If $$\sin \theta - \cos \theta = \frac{7}{17},$$ then find the value of $$\sin \theta + \cos \theta$$.

Given,  $$\sin \theta - \cos \theta = \frac{7}{17}$$

$$=$$>  $$\left(\sin\theta-\cos\theta\right)^2=\left(\frac{7}{17}\right)^2$$

$$=$$>  $$\sin^2\theta+\cos^2\theta-2\sin\theta\ \cos\theta\ =\frac{49}{289}$$

$$=$$>  $$1-2\sin\theta\ \cos\theta\ =\frac{49}{289}$$

$$=$$>  $$2\sin\theta\ \cos\theta\ =1-\frac{49}{289}$$

$$=$$>  $$2\sin\theta\ \cos\theta\ =\frac{240}{289}$$

$$=$$>  $$1+2\sin\theta\ \cos\theta\ =1+\frac{240}{289}$$

$$=$$>  $$\sin^2\theta+\cos^2\theta+2\sin\theta\ \cos\theta\ =\frac{529}{289}$$

$$=$$>  $$\left(\sin\theta+\cos\theta\right)^2=\left(\frac{23}{17}\right)^2$$

$$=$$>  $$\sin\theta+\cos\theta=\frac{23}{17}$$

Hence, the correct answer is Option B